Which one of the following is not correct ?

• Dimensional formula of thermal conductivity (K) is M¹L¹T^-3K^-1

• Dimensional formula of potential (V) is M¹L²T³A^-1

• Dimensional formula of permeability of free space (μ₀) is M¹L¹T^-2A^-2

• Dimensional formula of RC M⁰L⁰T^-1

In a lift moving up with an acceleration of 5ms^-2 dropped from a height of 1.25 m. The time taken by the ball to reach the floor of the lift is (g = 10 ms^-2)

• 0.3 s

• 0.2 s

• 0.16 s

• 0.4 s

3.

A gun fires a small bullet with kinetic energy K. Then kinetic energy of the gun while recoiling is

• K

• more than K

• less than K

• $\sqrt{\mathrm{K}}$

A truck accelerates from speed v to 2v. Work done in during this is

• three times as the work done in accelerating it from rest to v

• same as the work done in accelerating it from rest to v

• four times as the work done in accelerating it from rest to v

• ess than the work done in accelerating it from rest to v

Earth is moving around the sun in elliptical orbit as shown. The ratio of OB and OA is R. Then the ratio of Earth's velocities at A and B is

• R^-1

• $\sqrt{\mathrm{R}}$

• R

• R^2/3

A projectile is projected at 10 ms^-1 by making at an angle 60° to the horizontal. After some time its velocity makes an angle of 30° to the horizontal. Its speed at this instant is

• $\frac{10}{\sqrt{3}}$

• $10\sqrt{3}$

• $\frac{5}{\sqrt{3}}$

• $5\sqrt{3}$

From a fixed support, two small identical spheres are suspended by means of strings of length 1 m each. They are pulled aside as shown and then released. B is the mean position. Then the two spheres collide

• at B after 0.25 s

• at B after 0.5 s

• on the right side of B after some time

• on the right side of B when te strings are inclined at 15° with B

For which combination of working temperatures of source and sink, the efficiency of Carnot's heat engine is maximum ?

• 600 K, 400 K

• 400 K, 200 K

• 500 K, 300 K

• 300 K, 100 K

A solid cylinder of radius R made of a material of thermal conductivaty K₁ is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K₂. The two ends of the combined system are maintained at two different temperatures. Then there is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

• K₁ + K₂

• $\frac{{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

• $\frac{2{\mathrm{K}}_1 + {\mathrm{K}}_2}{4}$

• $\frac{{\mathrm{K}}_1 + 3{\mathrm{K}}_2}{4}$

Two stars A and B radiate maximum energy at the wavelength of 360 nm and 480 nm respectively. Then the ratio of the surface temperatures of A and B is

• 3 : 4

• 81 : 256

• 4 : 3

• 256 : 81